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Birds, Mozart, austerity, Thatcher
00:28:26
Birds + windows =? The BBC Quiz show The Unbelievable Truth reckons that more than 2...
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This week on the BBC's more or less programme, Tim Harford is back with nearly half an hour's worth of number Y Goodness. And in this download edition, we're going to try something a bit different. We're going to start with brand new items on whether it's possible to count how many birds die flying into windows and the numbers behind Mozart's the Magic Flute, before moving on to cover the Reinhart Rogoff spreadsheet mistake and Mrs. Thatcher by numbers in new longer versions.
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Hello, and welcome to a brand new series of More Or Less the programme, which serves up more numbers than a catering tin of numberetti spaghetti. This week, we bring you a statistical verdict on the premiership of Margaret Thatcher. We look at the mathematics of Mozart and we raise a quizzical eyebrow at David Mitchell's BBC Radio 4 quiz show, the Unbelievable Truth In America.
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Each day, over 2 million birds die, crashing into window panes.
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But first, spring has finally sprung. But, oh, no. There I was in my kitchen with the family, listening to the Radio 4 quiz the unbelievable Truth. As you may know, the aim of the game is to deliver a hilarious monologue on a given topic, almost all of which is false, and to smuggle five implausible truths cunningly concealed amidst the lies. And one of the unbelievable truths which made it past the panelists was this.
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In America, each day, over 2 million birds die, crashing into window panes. And at the end of that round, Mark, you've managed to smuggle three truths past the rest of the panel. The second truth is that in America, each day over 2 million birds die crashing into window panes.
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But I just found this unbelievable. Charlotte MacDonald, I said, this is one for a statistical sleuth like you.
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And, well, the story starts in 1990. That year, we were all dancing about to this kind of thing.
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Yo, vip, let's kick it. Is this relevant?
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I'm just setting the scene for you. Stop. And out in the us, an ornithologist was writing an article called Collisions Between Birds and Windows. He reasoned that there are a lot of buildings in the US and that most buildings have windows. So he looked up the number of buildings in the whole country, using U.S. bureau of Census data, and how many were there? About 100 million. He then thought, if we assume that over a year between one and 10 birds will hit windows on every building in the country and die, how many birds would that be?
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So that's multiplication plus assumption. Very neat. And so the fact was born that between 100 million and a billion birds die in the US. Each year hitting Windows.
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Yes, it features on a bird guide website and that's where the Unbelievable Truth team found it. They then took the highest number, a billion dead birds, divided it by 365 days and got their figure of more than 2 million a day. But I've spoken to leading bird window collision expert Professor Daniel Clem, and he thinks people shouldn't quote this number as if it was some kind of solid fact.
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He's just one expert and experts do disagree.
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Yes, but Professor Daniel Clem is the ornithologist who came up with the number in the first place.
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I don't believe that anyone should take those figures as facts. There was some quantitative basis behind it, but it wasn't to the level that one would consider those figures to be facts. It's probably likely, but I don't think any reasonable person should be using those figures as facts until we have more supportive evidence.
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Frankly, I'm shocked. What is the point of having a Radio 4 panel game built on truth and lies if the truths aren't true?
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Yeah, I know. That's what the news is for.
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David Mitchell, I trusted you and Charlotte. Thank you. I still trust you. Mozart's final opera, the Magic flute, premiered just 10 weeks before the composer's death and was the biggest popular hit of his life. With its pantomime storyline and catchy tunes, it's said to be one of the most accessible operas for the uninitiated. But there's an awful lot going on beneath the jokes and the musical notes. Oxford professor Marcus De Sotoy recently spoke at London's Royal Opera House about what he finds in the Magic Flute as a mathematician, more or less his. Charlotte MacDonald was in the audience.
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Welcome to our mathematical exploration of the Magic Flute and our musical journey through the world of mathematics. Obviously, music is highly emotional, but it's also got a lot of precision and mathematical structure in it. And Mozart loved mathematics around. There are lots of examples of him playing with numbers and kind of shapes. The Magic Flute, the last of his operas, is full of kind of numerical and geometric symbolism. So I wanted to sort of take the audience looking through my eyes or ears rather, at what I hear when I hear something like the Magic Flute. It's interesting that Mozart's other operas are very much to do with the human condition. Don Giovanni, Marriage of Figaro. They're very much set in the real world, but the Magic Flute is a much more abstract piece. It's a kind of rather a magical world. And that, I think, gives Mozart the freedom really to play A lot of games. Does anyone know the next number in this sequence? 1. 1, 2, 3, 5, 8. 13, 21. Yes. If you read the Da Vinci Code, it's one of the things you have to crack in the Da Vinci Code. These are called the Fibonacci numbers because you add the two previous numbers together to get the next one in the sequence. That's the rule. The way the Magic Flute is divided up. The first act is divided into eight musical pieces. The second act is divided into 13 musical pieces. Eight plus 13 gives you 21 in total, three Fibonacci numbers. Now, was that just a coincidence? I think not. Mozart had joined the Freemasons seven years earlier. And the Masons, of course, have a lot of connections to mathematics through sort of geometry and numbers. The Masons, after all, built things, and so mathematics is key to that. So a lot of their rituals have mathematics in it. Now we move through to the importance of the number three. In this opera, we find lots of threes. We had the three ladies. It's also a very important number for the Masons. And Mozart uses this number three to indicate kind of the connections with the masons. One of the rituals that an initiate has to go through is to knock a rhythm on the door of the lodge. And it's three notes in a particular rhythm and done three times. And we hear this triple chord again and again throughout this opera. So here is the triple chord. I think sometimes I've chosen to be a mathematician because when you do mathematics, there's a feeling like you can leave something permanent after your death, because the power of proof means that something you've proved will be true forever. And I think Mozart's music, perhaps more than anybody's, has that kind of eternal truth about it. It transcends space and time. And he really did achieve life after death through his music.
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Professor Marcus De Sotoy, talking to Charlotte MacDonald about the mathematical properties of Mozart's opera the Magic Flute. Let me take you back to January 4, 2010, the Marriott Hotel in Atlanta, the annual meetings of the American Economic association, where the world's leading economists gather to deb, debate, discuss and economise. Two respected professors, Carmen Reinhart and the former chief economist of the International Monetary Fund, Ken Rogoff, are presenting a research paper called Growth in a Time of Debt. As with all such conference papers, it's brief and was never meant to be a peer reviewed research paper, but it will pack a real punch. Reinhart and Rogoff had been gathering together a large set of historical data and comparing the size of a country's debt to the size of a country's economy. Specifically, when government debt passes, 90% of the country's GDP growth is dramatically lower.
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The paper was of interest from the very start.
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Michael Ash, a professor of economics and public policy at the University of Massachusetts
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Amherst, it set this image of a threshold or cliff at 90% public debt to GDP. And beyond that, woe unto the country that passes.
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Now, Michael Ashe had an assignment for his students.
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We asked the students to replicate what they feel is an important paper in the economics literature. And our student, Thomas Herndon chose Growth in a Time of Debt as his student project.
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While Thomas Herndon was getting stuck into his homework, the world was going through an economic crisis and an intense political argument. Most developed countries were in recession and not coincidentally, debt was growing rapidly, sometimes because of deliberate attempts to stimulate the economy, sometimes just because tax revenues were falling and more people were claiming benefits. Which led to a now familiar let debt increase in the hope of promoting economic growth and getting out of recession, or cut spending and raise taxes aggressively to get public debt under control. And not surprisingly, Carmen Reinhart and Ken Rogoff's statistical discovery was in the spotlight. The paper came out a few months before the UK general election. George Osborne talked about it on the campaign trail. Here's a dramatic reenactment. The latest research suggests that once debt reaches more than about 90% of GDP, the risks of a large negative impact on long term growth become highly significant. And it wasn't just Mr. Osborne. Oli Ren, the EU's commissioner for economic and monetary affairs, has mentioned a 90% debt limit, as widely acknowledged, while making the case for belt tightening in the Eurozone periphery. And here's Paul Ryan, vice presidential nominee in 2012 and a big hitter for the Republican Party, presenting his case for cuts in spending.
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You know, the economists tell us, when your debt gets to 90% as a share of your economy, you start slowing down and we stagnate.
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But while America voted, the Eurozone tottered and politicians across the developed world debated whether spending cuts and tax rises were an essential measure for getting debt under control or a cricket bat to the groin of the world economy, all with a Reinhart and Rogoff result hanging in the air, Thomas Herndon's homework assignment wasn't going well.
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My heart sank. Really. I thought that I must have made some gross error somewhere.
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Try as he might, Thomas just couldn't replicate the author's key finding the average GDP growth of highly indebted countries.
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I had a talk with Michael and he was just basically like, all right, Thomas, there's two variables here and you're taking an average. It shouldn't be that hard. You really need to go get this sorted out immediately.
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But he tried and he tried and he just couldn't get the sums to add up. Thomas's professors took a closer look and they realized they couldn't either.
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We had this puzzle that we were unable to replicate the results as Reinhart and Rogoff published them, and that really got under our skin.
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And so what was the next step to approach Reinhart and Rogoff?
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Yes, the course ended and we encouraged Thomas to continue his research. He contacted Reinhart and Rogoff and they kindly provided the actual working spreadsheet that they had used to produce the results.
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In the paper, with the author's numbers and methodology in hand, came a revelation. Thomas went straight to the part of the spreadsheet which contained the troublesome calculation.
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I immediately saw the spreadsheet error. They left out five countries out of the 20 countries. They had left out Australia, Austria, Belgium, Canada and Denmark. And you know, they say seeing is believing, but I almost didn't really believe my eyes.
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Oops. But Thomas and the professors then found other issues with growth in a time of debt, which had more of an impact on the famous results than this basic spreadsheet error. The first was the fact that some data was missing for some countries. Now, Reinhart and Rogoff say they were assembling the data series bit by bit. And at the time they presented the paper at the American Economic Association Conference, good quality data on post war Canada, Australia and New Zealand simply weren't available. Nevertheless, the emission made a substantial difference. But Michael Asch says he and his colleagues also didn't like the way that Reinhart and Rogoff averaged their data. They say that one bad year for a small country such as New Zealand was blown out of proportion.
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New Zealand's single year, 1951, at minus 8% growth, is held up with the same weight as Britain's nearly 20 years in the high public debt category at 2.5% growth, or Greece's nearly 20 years in. In the high public debt category at 2.5% growth, those are given equal weight. So you average one year for New Zealand at minus eight, with 20 years for Britain at two and a half, and you say, oh, those average out to about minus three. I think that's a mistaken way to examine these data.
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Now, there's no black and white here because there are downsides to the obvious alternatives too. But still, Reinhart and Rogoff's averaging method was controversial and it too made a big difference. All these results were published by Thomas Herndon and his professors on 15 April as a draft working paper. They find that high levels of debt are still correlated with lower growth, but the most spectacular results from the Reinhart and Rogoff paper disappear. The correlation is much gentler, and there are lots of exceptions to the rule. Carmen Reinhart and Ken Rogoff weren't available to be interviewed, but they did send us a statement.
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Here's an we are grateful to Herndon et al. For the careful attention to our original paper and for pointing out an important correction to figure two of that paper. We do not, however, believe this regrettable slip affects in any significant way the central message of the paper, or that
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in our subsequent work accidents do happen and science progresses through the identification of previous mistakes. But was this a particularly expensive mistake? It's certainly true that pro austerity politicians have sometimes leaned on the Reinhart Rogoff results, but arguably they were already committed to the idea of austerity and simply found that Reinhart and Rogoff had provided a nice quotable statistic. For instance, George Osborne had argued the case for austerity before the Reinhart and Rogoff paper even existed. But Daniel Hammermesh, a professor of economics at Royal Holloway University of London, says that in the end, even economics papers sometimes matter. I don't think jobs were destroyed because of this, but it provides an intellectual rationalization for things that then affect how
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people think about the world.
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And how people think about the world, especially politicians, eventually affects how the world works. Now, let's not fool ourselves that discovering a spreadsheet error will end the debate over austerity. Here's Meghan McCardle, special correspondent for Newsweek and the Daily Beast. There is other research showing that you can have these slowdowns when you get to high levels of debt. And I think that the way that this one 90% figure got wrapped into some sort of scientific proof of people's prior beliefs about taxation and spending and government debt is sort of unfortunate because it's now obscured what remains a very live debate about how fast we should be cutting, how far we need to get our debt down, and how much all of this matters. Meanwhile, Thomas is cracking on with the New Terms classes, which got underway this week with probably a newfound confidence.
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Yeah, I never for a second thought that the world would be interested in my econometrics replication paper. Never for a second. And I'm incredibly honored to have been able to make this, you know, whatever small contribution I could to the discussion on such an important policy issue.
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And the next time some fascinating statistical discovery blazes its way into the political debate, bear it in mind. But remember that no single empirical study will be conclusive in a complex world, even if the spreadsheet rows do add up. You're listening to More or less on BBC Radio 4. If there are any numbers which don't seem to add up to you, email us at more or lessbc.co.uk. if we're non+2, we'll launch an immediate and thorough investigation. Baroness Margaret Thatcher was Britain's first female Prime Minister and one of the most influential political figures of the 20th century. She was a pioneer of free market economics, helping to spread the idea around the world. But as her death last month reminded us, the Iron lady had enthusiastic supporters and impassioned critics. Both are pretty confident in their beliefs about what she did. But what did the data tell us?
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And the mounted police are going in again
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at a full gallop, right up the hill in the face of the missiles.
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The miners strike in 1984. The battle between Mrs. Thatcher and the miners defined her premiership. To her supporters, she defeated the overpowerful unions. To her critics, she destroyed whole swathes of British industry, such as mining and manufacturing. A look at the numbers certainly confirms Baroness Thatcher's reputation as the ultimate union basher. In the 1990s, after a 10 year dose of Thatcherism, there were just 6.5 million days lost to strikes. The a huge decline. It's also true that the mining industry shrank dramatically in the 80s. But was Mrs. Thatcher responsible? Professor Andrew Oswald, an economist at Warwick University, looks at employment trends over decades and internationally.
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At its peak, there were more than 1 million miners in Britain. This is before the Second World War. Now there are only a few thousand. That huge sweep down in the giant graph that economists use to draw mining employment was really nothing to do with Mrs. Thatcher. She may have intensified the drop off in mining employment, perhaps in the late 80s after the giant confrontations. But it's not sensible to blame Mrs. Thatcher for the decline of the mining industry. This is a trend visible all over the Western world.
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Nor, Andrew Oswald says, do the data support the popular view that Thatcher killed off British manufacturing.
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The decline in manufacturing as a proportion of total employment in a country like Britain, that's a very long standing. And Mrs. Thatcher couldn't make much impact on that downward trend. She's viewed historically as the enemy of manufacturing industry. But I think most of that criticism is incorrect. These are very powerful historical trends. As we get richer and richer in Western countries, we live more by our wits than by our skill at producing physical items.
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Mrs. Thatcher is also painted as the great tax slasher, a portrait she partly contributed to herself.
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How often do you hear people say, look how much they've taken from my pay packet. They don't work for the chance of the Exchequer, they work for their families. So we've got to cut the tax on earnings and the tax on skill, give our people incentives, and once again, Britain will be back in the race.
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But what do the statistics show? It's true that Mrs. Thatcher cut direct taxes. When she came to power, the top rate of income tax was 83%. That was on incomes over the equivalent of about 155,000 pounds today. By the time she left government, the top rate of tax was 40% and basic rate tax fell from 33 to 25%. But the amount raised by indirect taxes, such as beer and cigarette duty, or VAT, almost doubled. The VAT rate increased from 8% to 15%. So what does this mean for public spending? Did she roll back the frontiers of the state? Not as much as her supporters and critics like to believe. Public spending actually went up in real terms under Mrs. Thatcher. High unemployment meant she had to spend more on benefits. But relative to the economy, public spending did fall during her time in office, from 44% to 39% of GDP. During Margaret Thatcher's premiership, critics believed she had a secret plan to dismantle the nhs. And. And this was her famous response, the
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National Health Service is safe with us,
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but the idea that she starved the NHS of money has stuck. And that's odd, because, contrary to popular belief, Mrs. Thatcher more or less maintained the same steady rate of increase in state health spending as her predecessors. Here's Alyssa Goodman, professor of Economics at the Institute of Education.
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I certainly look back on that era with the impression that there were a lot of cuts in health spending. But when you actually look at the figures, that isn't the case. Health spending grew both in real terms and slightly as a share of the economy. Education is slightly different as a share of the economy. It did fall back slightly, but on the other hand, it was also a time of falling pupil numbers. And I think that partly offsets that slight Trend.
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In the 1980s, pupil numbers went down from well above 13 million to well below 11 million. So, in fact, though public spending on education fell, pupil numbers fell faster. So Mrs. Thatcher's government actually spent More money per child. Next, housing. Margaret Thatcher was accused of causing a housing crisis as she sold off thousands of council homes and didn't build many new ones. But the numbers on house building make interesting reading. Elissa Goodman says the key date turns out to be not Mrs. Thatcher's election in 1979, but four years earlier, 1975.
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The chart I'm looking at starts in 1956 and goes forward to the year 2000. And what I can see on it are two particularly large peaks in the mid-1960s and also the mid-1970s, when we were spending around two to two and a half percent of our national income on public investment, on housing alone. The dramatic thing about the picture is also that after 1975, the level absolutely collapses. It just disappears away. Clearly in the years after the Second World War and arguably the decades, there was a lot of post war reconstruction to be done and slum clearance and so on. But it might have been hard to imagine a situation where that level of house building could have been maintained in the longer term.
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But strikingly, Mrs. Thatcher didn't increase the levels of public sector investment in housing, nor have any of her successors. Now, what about the common claim that Britain under Margaret Thatcher became a more unequal society? Yes, the numbers say this did happen. Here's Professor Nick Crafts, economic historian at Warwick University. If we look at the mid-1970s, the top 10% were probably earning two and a half times the level of the bottom 10%. By the end of the 80s, beginning of the 90s, that ratio had moved to about three and a half times and was still continuing to rise. Taking account of inflation, the incomes of the top 10% grew about 60% during Mrs. Thatcher's time in office, while the incomes of the poor hardly grew at all. And on some measures they shrank. Now, Mrs. Thatcher wasn't the only cause, but policies over which she had discretion, such as the reduction of the top rate of tax and the break of the earnings link by which benefits had been uprated, did increase the gap. For her critics, that complaint goes hand in hand with another, that Mrs. Thatcher was responsible for one of the worst periods of unemployment in modern British history.
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The latest unemployment figures show a rise of 128,000, taking the total to a
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new record, nearly three and a quarter million. The news brought the comment a great disappointment from Mrs. Thatcher. The numbers were unquestionably high and the experience for many people, miserable. But what can we tell from the data when we look at the trends on the graphs? The rises and falls in unemployment over the long term compared with those in other countries, including those with policies quite different from her own. It's actually difficult to identify a specific Thatcher effect. Here's economist Andrew Oswald.
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Mrs. Thatcher inherited a growing unemployment problem. The 50 years from 1950 to the year 2000, unemployment in great Britain is like a gently rising escalator with a lot of wiggles along the way. So there's a strong upward trend. What did happen in the year of 1979 was there was a very large rise in the price of oil and that undoubtedly pushed up unemployment a lot. Over the ensuing, let's say, two or three years, that trend was visible all over the Western world. Her government was very strong on controlling inflation and that probably added an upward twist to the unemployment. But most of the rise in joblessness, I think, can be traced back to what happened in the Middle east, not to Mrs. T herself.
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And something else happened to UK unemployment later. In the 1980s. It fell sharply and far more quickly than elsewhere in Europe. And still to this day, employment in Britain is higher than in most European economies, a fact which some attribute to the labour market flexibility that Mrs. Thatcher's government introduced. So does this mean that the net effect of Margaret Thatcher's time in office, and perhaps this is her supporter's boldest claim, is that she transformed a sick man of Europe into, into a dynamic enterprise economy? Well, the numbers show it is true that economic growth was decent and improved the UK's position in relation to its European rivals. Finally, in 1978, before she was elected, Margaret Thatcher didn't shy away from the issue of immigration.
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People are really rather afraid that this country might be rather swamped by people with a different culture.
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A committee had estimated, Sochi said, that there would be 4 million people of the new Commonwealth or Pakistan in the UK by the end of the century. This interview and Margaret Thatcher's use of the word swamped caused controversy. But by the end of the century, had she been proved right on the numbers? Well, yes, the 2001 census showed 4.6 million foreign born people living in Britain. This may be the first time in history that a projection about immigration has been close to correct. So to sum up, the list of dramatic things Mrs. Thatcher is said to have done for good or ill, is long. The numbers tell us that the list of things she really did do is rather shorter. Yes, she improved Britain's economic performance. Yes, she crushed the unions. And yes, she made Britain a more unequal place. Her record as a cutter of education and health budgets and a slayer of traditional industry is less clear cut. But in the end, for both friend and foe, the image of Mrs. Thatcher, perhaps because it was so vivid, perhaps because it was even cultivated, far exceeds the evidence of the Numbers. And that's all we have time for this week. But if you subscribe to Our download via BBC.co.uk More or less, you'll be able to ensure that you never miss another programme. And the website is also the place to read more or to send us your comments and your questions. Goodbye.
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More or Less was presented by Tim Harford, produced by Ruth Alexander and edited by Richard Varden, with special thanks to Michael Black Basland and Andrew Dillnott, whose journalism greatly contributed to the item on Margaret Thatcher by numbers. There are many more Radio 4 and World Service news and current affairs programmes to download for free. Find these on the BBC website.